1. Field of the Invention
The present invention relates to a pattern inspection apparatus, a image registration method, or a computer program for applying the method. For example, the present invention is applicable to a pattern inspection technique that inspects a pattern defect on a mask pattern or a master pattern used in fabricating semiconductor devices, and an inspection apparatus that detect a defect on fine patterns of a photomask, a wafer and a liquid crystal substrate (LCD).
2. Description of Related Art
In recent years, a LSI line-width required for semiconductor devices has been shrinking to tens of nanometers. These semiconductor devices are manufactured by exposing or projecting a circuit pattern on a wafer by using a reduction-magnification exposure projection apparatus such as a stepper while using a master pattern (called a mask or a reticle, and will be called a mask hereinafter) on which a circuit pattern is written. Therefore, in order to fabricate a mask for projecting fine circuit patterns on a wafer, a pattern writing apparatus is employed that writes a fine circuit pattern. Alternatively, a circuit pattern could be directly written onto a wafer by the writing apparatus. In addition to an electron beam writing apparatus, a laser beam writing apparatus might be also applicable.
Since LSIs require enormous fabrication cost, an improvement in yield is crucial in semiconductor business. However, line-width of LSI has been shrinking downto tens of nanometers. The yield loss in semiconductor devices is significantly due to a pattern defect on a mask. In particular, critical-dimension (CD) error is so detrimental that much tighter CD uniformity is necessary. Therefore, a pattern inspection apparatus which inspects those defects is necessary to guarantee the quality of a mask.
As to a conventional pattern inspection apparatus, the following is known as pattern inspection methods: ‘die-to-die inspection’ that compares optical image data obtained by capturing images of the same patterns at different positions on the same mask, and ‘die-to-database inspection’ that inputs writing data (CAD data) which is generated by converting GDSII data to be input by a writing apparatus, generates a reference image based on the inputted writing data, and compares a reference image with an optical image obtained by capturing the image of the pattern. In the inspecting methods of the inspection apparatus, a target workpiece is placed on a stage to be scanned by a flux of light while the stage is moving to scan the workpiece.
The target workpiece is irradiated with a flux of light from a light source and an illumination optics system. Light transmitted through the target workpiece or reflected by the target workpiece is focused on a sensor through an optical system. The image captured by the sensor is transmitted to a comparison circuit as measurement data. In the comparison circuit, after registration of the images, the measurement data is compared with reference data based on an appropriate comparison algorithm. When the measurement data is significantly different from the reference data, it is judged to be a pattern defect.
In order to perform inspection as described above, image registration between a reference image and an optical image is strictly required. It is, therefore, preferable to correct only systematic position errors, such as stage misplacement due to an error due to expansion and contraction, and a rotation error along the axis of an X-Y stage. In other words, it is preferable not to correct errors that are local and random, such as a pattern defect. Performing correcting as described above is required for detecting minute defects.
As a image registration method, for example, a technique is disclosed that calculates an amount of displacement and a sum of gray level differences between a reference image and an optical image by using a least-squares method (refer to, e.g., Japanese Unexamined Patent Publication No. 11-153550 (JP-A-11-153550)). For example, as shown in the equation (1) below, there is a mathematical model in which an optical image is represented by shifting and interpolating the reference image by the amount of misalignment. In the equation (1), S (x, y) shows a gray level of an optical image, and U (x, y) shows a gray level of a reference image. Parameters to calculate are the amount of shift: (x0, y0), an offset of gray level: ε0, and an image transmission loss ratio: ε1. However, since this mathematical model is based on a simple shift, it is not sufficient to compensate a placement error from image distortion, and/or rotation.S(x,y)=−ε0+(1−ε1)·U(x−x0,y−y0)  (1)
The following equation (2) can be obtained by calculating a linear approximation of the equation (1). The unknown parameter has four degrees of freedom.ε0+ε1U+x0·∂U/∂x+y0·∂U/∂y=U−S  (2)
Further, a method that interpolates the target image data by use of image data of four neighboring points of the image data is described in a reference (refer to, e.g., Image Analysis Handbook, at pp. 442 to 443, University of Tokyo Press, first edition issued on Jan. 17, 1991).
As to the equation (2), a solution, which is not heretofore known, can be considered as follows: Normalizing the size of an image frame to 1 and interpolating target image data by use of a bilinear interpolation method of the four points stated above, the equation (2) can be modeled to the following equation (3).
                              U          -          S                =                                            (                              1                -                x                            )                        ·                          (                              1                -                y                            )                        ·                          (                                                ɛ                  0                                      (                    1                    )                                                  +                                                      ɛ                    1                                          (                      1                      )                                                        ⁢                  U                                +                                                      x                    0                                          (                      1                      )                                                        ·                                                            ∂                      U                                        /                                          ∂                      x                                                                      +                                                      y                    0                                          (                      1                      )                                                        ·                                                            ∂                      U                                        /                                          ∂                      y                                                                                  )                                +                      x            ·                          (                              1                -                y                            )                        ·                          (                                                ɛ                  0                                      (                    2                    )                                                  +                                                      ɛ                    1                                          (                      2                      )                                                        ·                  U                                +                                                      x                    0                                          (                      2                      )                                                        ·                                                            ∂                      U                                        /                                          ∂                      x                                                                      +                                                      y                    0                                          (                      2                      )                                                        ·                                                            ∂                      U                                        /                                          ∂                      y                                                                                  )                                +                      x            ·            y            ·                          (                                                ɛ                  0                                      (                    3                    )                                                  +                                                      ɛ                    1                                          (                      3                      )                                                        ·                  U                                +                                                      x                    0                                          (                      3                      )                                                        ·                                                            ∂                      U                                        /                                          ∂                      x                                                                      +                                                      y                    0                                          (                      3                      )                                                        ·                                                            ∂                      U                                        /                                          ∂                      y                                                                                  )                                +                                    (                              1                -                x                            )                        ·            y            ·                          (                                                ɛ                  0                                      (                    4                    )                                                  +                                                      ɛ                    1                                          (                      4                      )                                                        ·                  U                                +                                                      x                    0                                          (                      4                      )                                                        ·                                                            ∂                      U                                        /                                          ∂                      x                                                                      +                                                      y                    0                                          (                      4                      )                                                        ·                                                            ∂                      U                                        /                                          ∂                      y                                                                                  )                                                          (        3        )            
As shown in the equation (3), adding this interpolation scheme makes it possible to correct the placement error resulting from image distortion, and/or rotation which is not sufficient to be corrected by using the model of the equations (1) and (2). However, a four-point weighted interpolation scheme increases necessary parameters to 16 (four times the above-mentioned model) and calculation time accordingly, as shown in the equation (3). Furthermore, in addition to the problem of increasing the number of the unknown parameters, there exists another problem that instability in the calculation result occurs when the in case for sparse figure density is sparse.